Market for Wins in Baseball

This article on the art of pitch framing, and its subjection to statistical measurement, is excellent, and you should read it. 

In it the author says that wins go for $5 million on the free agent market.  But it isn’t the case that an average, 81-81 team has a $405 million payroll, nor is such a team made entirely or mostly of players who have not yet hit free agency.  What he means is that wins above replacement run at $5 million a piece.  If a player brings you two wins per year above what you would get if you replaced him with a replacement-level player (basically, minimum major league quality players- a backup or a top minor-leaguer), he costs you $10 million per year. 

You could go, let’s say, 50-112 with a team of 25 MLB-minimum, $300 thousand replacement players.  That’s $7.5 million in salary, or $500,000 per win.  Teams have good players who haven’t hit free agency yet, and are playing for cheap, not the minimum (and some sign their players in free agency at an equilibrium price that accounts for but is less than the $5 million per win free-market rate), so you could actually build a team that’s better than replacement level without spending much money, if that were your goal. 

I conclude that wins take on increasing marginal utility.  Going from 59 to 60 wins is of little value; going from 69 to 70 doesn’t much matter.  Moving from 92 wins to 93, or 93 to 94 is frantically, desperately necessary.  Wins at that margin are in dire demand.  Past the point at which you’ve secured a playoff spot, extra wins are a proxy for likely post-season success, and as such continue to be desperately needed.

(I don’t care if you show me some kind of chart that says regular season win totals are weakly correlated to post-season success, not at all correlated, inversely correlated, or correlated in terms of imaginary numbers.  Nobody is ever going to say “let’s make sure we’re good enough for the post-season and stop spending at that point.  Let our competitors have better players, because the playoffs is a crapshoot anyway.”  Obviously, teams do limit their payrolls; some teams value that extra win more than others, but it isn’t the case that the randomness of short makes teams less intense about getting better at a certain margin.  Anyway, I said wins are a proxy.  Maybe teams try to build themselves specifically to win in the playoffs.  That won’t really change the analysis.  It’s not like you can time things precisely and say “we’ve bought 88 wins, we’re in the playoffs,” anyway.  As the knight on Monty Python says of Camelot, “it’s only a model.”)

So at the highest level, teams are intensely competing over that extra half-percentage-point chance of winning the World Series.  At a certain point, of course, extra spending takes on diminishing marginal utilities in terms of percentage chance of winning the World Series, but those extra percentage points themselves probably take on increased marginal utility.  Baseball people, fans and culture have assigned enormous subjective value to winning the World Series, as opposed to just winning a high quantity of games, and their actions reflect that value system.  They also of course value the process of trying to win, as they have to in order to avoid insanity in a random business, but that does not affect the question.

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